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Need a little help with math notation

  1. Jan 1, 2010 #1

    Oddbio

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    In my math book, I am seeing a few things like this:

    For any set I, and any family [itex](A_{i})_{i\in I}[/itex] of open subsets, the union [itex]\cup_{i\in I}A_{i}[/itex] is also an open set (any union of open sets is open);

    I also see one later like:
    [tex]\cap^{n}_{i=1}A_{i}[/tex]

    But I always thought that a union (and intersection) had to be of the form:
    [tex]A\cup B or A\cap B[/tex]

    So the first one has nothing on the left side, same as the second one.. but the second one also has super and sub-scripts?
    Do they mean something completely different than "union" and "intersection"?

    I apologize if this is a trivial question.. it sure feels like it.
     
  2. jcsd
  3. Jan 1, 2010 #2

    nicksauce

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    The notation of the form [itex]\cup_{i\in I}A_{i}[/itex], means that you have a family of sets A_i, and you do the union of all of them. i.e.,

    [tex]\cup_{i\in I}A_{i} = A_1\cup A_2\cup...[/tex]
     
  4. Jan 1, 2010 #3

    nicksauce

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    Actually I guess that isn't strictly true, since the family of sets doesn't have to be countable, but I hope you get the idea.
     
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